"The gravity of the offenses of which she is accused does not allow an alternative to custody", the judge wrote in his decision.
"Nothing that Ahed Tamimi has done can justify the continuing detention of a 16-year-old girl".
The charges relate to the video and two other incidents, and could result in her spending years in jail, as well as months as she waits for her trial.
The PPS said that the soldiers invaded many homes in several parts of the West Bank governorate of Bethlehem, and abducted eight Palestinians, identified as Bilal Khader Salama, 24, As'ad Darwish, Mo'men Malash, Mohammad al-Asakra, Awad al-Asakra, Adam Eyad al-'Amour, 17, Mahmoud Salem al-Badan, and former political prisoner Yasmin Abu Srour.
There are frequent tensions between settlers in the Nablus area and Palestinians.
Mr Heeran noted that she was arrested from her home in the middle of the night, interrogated without a relative or lawyer present, and is now held outside the occupied territories in what he said contravenes global humanitarian law.More news: United States lawmaker proposes ban on Huawei and ZTE
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Another Palestinian was also wounded, reports said. "That would be captured on camera and then that is broadcast overseas", he said.
PPS said in a statement that Israeli forces detained eight Palestinians from the southern West Bank city of Bethlehem, three from the central West Bank Ramallah district, two from the southern West Bank al-Arroub refugee camp near Hebron, one from Tulkarm, one from Nablus and another from Jenin, all in the northern West Bank.
International observers and human rights groups, such as Amnesty International, have called for the young woman's immediate release. "There is justice within the Military Court", he said.
"Ahed's detention and prosecution in Israel's military court system is not exceptional, but provides a clear example of how Israeli military law and military courts are used to control an occupied Palestinian population", Brad Parker, a lawyer at Defense for Children International, told Sky News.
Children like Ahed may be exposed to physical violence and harsh interrogations including being blindfolded or sleep deprivation, he said.
Ahed Tamimi was hailed as a hero and an icon of the Palestinian struggle against the Israeli occupation.